Problem: On the way to school, Karen became fixated on the puzzle game on her phone!

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The game is played as follows. In each level, you have a grid with n rows and m columns. Each cell originally contains the number 0.

One move consists of choosing one row or column, and adding 1 to all of the cells in that row or column.

To win the level, after all the moves, the number in the cell at the i-th row and j-th column should be equal to gi, j.

Karen is stuck on one level, and wants to know a way to beat this level using the minimum number of moves. Please, help her with this task!

Input

The first line of input contains two integers, n and m (1 ≤ n, m ≤ 100), the number of rows and the number of columns in the grid, respectively.

The next n lines each contain m integers. In particular, the j-th integer in the i-th of these rows contains gi, j (0 ≤ gi, j ≤ 500).

Output

If there is an error and it is actually not possible to beat the level, output a single integer -1.

Otherwise, on the first line, output a single integer k, the minimum number of moves necessary to beat the level.

The next k lines should each contain one of the following, describing the moves in the order they must be done:

  * row x, (1 ≤ x ≤ n) describing a move of the form "choose the x-th row". 
  * col x, (1 ≤ x ≤ m) describing a move of the form "choose the x-th column". 



If there are multiple optimal solutions, output any one of them.

Examples

Input

3 5
2 2 2 3 2
0 0 0 1 0
1 1 1 2 1


Output

4
row 1
row 1
col 4
row 3


Input

3 3
0 0 0
0 1 0
0 0 0


Output

-1


Input

3 3
1 1 1
1 1 1
1 1 1


Output

3
row 1
row 2
row 3

Note

In the first test case, Karen has a grid with 3 rows and 5 columns. She can perform the following 4 moves to beat the level:

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In the second test case, Karen has a grid with 3 rows and 3 columns. It is clear that it is impossible to beat the level; performing any move will create three 1s on the grid, but it is required to only have one 1 in the center.

In the third test case, Karen has a grid with 3 rows and 3 columns. She can perform the following 3 moves to beat the level:

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Note that this is not the only solution; another solution, among others, is col 1, col 2, col 3.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
const int siz = 5e3 + 5;
int t, n, m, f[siz][siz];
int32_t main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cin >> n >> m;
  for (int i = 1; i <= n; i++)
    for (int j = 1; j <= m; j++) cin >> f[i][j];
  vector<pair<int, int> > row, col;
  int op = 0;
  for (int i = 1; i <= n; i++) {
    for (int j = 1; j <= m; j++) {
      if (f[i][j] == 0) continue;
      for (int z = 0; z < 2; z++) {
        int mn = 1e9;
        for (int k = 1; k <= n; k++) mn = min(mn, f[k][j]);
        int mn2 = 1e9;
        for (int k = 1; k <= m; k++) mn2 = min(mn2, f[i][k]);
        if ((mn != 0 and n >= m) or (mn != 0 and mn2 == 0)) {
          col.push_back({j, mn});
          op += mn;
          for (int k = 1; k <= n; k++) f[k][j] -= mn;
        } else {
          if (mn2 > 0) row.push_back({i, mn2});
          op += mn2;
          for (int k = 1; k <= m; k++) f[i][k] -= mn2;
        }
      }
      if (f[i][j] != 0) return cout << -1 << endl, 0;
    }
  }
  cout << op << endl;
  for (auto x : row) {
    int cnt = x.second, r = x.first;
    while (cnt--) cout << "row " << r << endl;
  }
  for (auto x : col) {
    int cnt = x.second, r = x.first;
    while (cnt--) cout << "col " << r << endl;
  }
}